As with any panoramic photo created by a standard camera and lens you will need an amount of overlap to achieve a seamless final product. In many cases I use about 1/3 of the image as an overlap to create a final image.

You might be familiar with an option that Adobe Photoshop has to stack images and remove parts of the image that are unwanted. It does this by creating a smart object that contains all of the stacked images that you shot, then Photoshop automatically identifies areas that are similar between the photos, and removes the elements that change between the shots.

While I do not know as a fact that the Gigapan device uses the same logic, I would assume that is the only technically possible way to achieve this without manual intervention.

Here is more detail on how Adobe Photoshop CS4 accomplishes this task: Adobe.com

The Gigapan stitcher is relatively simple and works best with well behaved photos. It's biggest merrit is that it can stitch large amounts of photos that most other programs cannot.

My Gigapan mount was slightly slanted so every picture that I took was rotated a few degrees . This was something that the Gigapan stitcher could not handle at all. This would not normally not be any problem for Photoshop Elements if it wasn't for the number of photos in the panorama.

My recommendation is Photoshop (Elements) for panoramas of a few (less than eight) photos and the Gigapan Stitcher for larger number of photos.

I have not interests in either company.

Good luck

ps
Now that I read your question one more time I might have missunderstood the question. You were asking about movements in the picture and not of the camera. Sorry. Sadly the Gigapan Stitcher that I have used could not handle this at all. As stated before it is a very simple program; feature wise. ds